Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups |
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| Authors: | Gennian Ge Malcolm Greig Jennifer Seberry Ralph Seberry |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027 Zhejiang, P. R. China;(2) Greig Consulting, 317–130 Eleventh St. East, North Vancouver, B.C., V7L 4R3, Canada;(3) Centre for Computer Security Research, SITACS, University of Wollongong, Wollongong, NSW 2522, Australia;(4) 7 Leeds Place, Turramurra, NSW 2074, Australia |
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| Abstract: | We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v,3,λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated
(v,3,λ) BIBD plus λ≡ 0 (mod|G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if v = 3 and the Sylow 2-subgroup of G is cyclic, then also λ≡ 0 (mod2|G|). |
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| Keywords: | Generalized Bhaskar Rao design Cyclic group divisible designs |
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